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Relative magnetic field analysis on Casson dusty fluid of two-phase fluctuating flow over a parallel plate: second law analysis

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Abstract

Due to the important application of magnetohydrodynamic in cancer tumor treatment, magnetic drug targeting, magnetic endoscopy, magnetic devices for cell separation, fluid pumping in industrial and engineering developments, and adjusting blood flow during surgery. Therefore, we investigate the relative magnetic field analysis of the two-phase fluctuating flow of Casson dusty fluid over a parallel plate. More exactly, the relative magnetic phenomena are fixed relative to the fluid (MFFRF) or fixed relative to the plate (MFFRP). Moreover, the entropy generation and Bejan numbers analysis are also considered for both MFFRF and MFFRP. The mathematical modeling was established as the set of partial differential equations for dusty Casson fluid. Buckingham’s pi theorem is used to find out the dimensionless variables, to make our system dimensionless. The perturb solution is to find out by incorporating Poincare–Lighthill perturbation technique. To know in-depth different parameters, the graphical results for both velocities are plotted with the help of Mathcad-15 software. It is observed that the relative magnetic field plays an important role in the fluid as well as particle motion. The relative magnetic field is affecting the entropy generation as well as the Bejan number. This study will help out in the adjusting of blood flow during surgery and fluid pumping in industrial and engineering process.

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Data availability

All the data are used are available in the manuscript.

Abbreviations

\(C_{{\text{p}}}\) :

Heat capacity at a constant pressure

\(d\) :

Distance between two plates

Gr:

Thermal Grashof number

\(g\) :

Gravitational Acceleration

\(k\) :

Fluid thermal conductivity

\(B_{0}\) :

Applied magnetic field

\(\sigma\) :

Electrical conductivity

Pr:

Prandtl number

\(t\) :

Time

\(u(y,t)\) :

Velocity of the fluid

\(K_{1}\), \(K_{2}\) :

Dusty fluid variable

Br:

Brinkman number

\(\Omega\) :

Dimensionless temperature difference

\(U\left( t \right)\) :

Free stream velocity

\(M\) :

Magnetic parameter

\(\theta\) :

Dimensionless temperature of the fluid

\(v(y,t)\) :

Dust particle Velocity

\(\beta_{{\text{T}}}\) :

Volumetric coefficient of thermal expansion

\(\varepsilon_{1}\) :

Relative magnetic parameter

\(T\) :

Temperature of the fluid

\(T_{\infty }\) :

Ambient temperature

\(T_{{\text{w}}}\) :

Wall temperature

\(q_{{\text{r}}}\) :

Radiation heat flux

\(\beta\) :

Casson fluid parameter

\(K_{0}\) :

Stock’s resistance coefficient

\(\rho\) :

Fluid Density

\(N_{0}\) :

No of density of the dust particle

Pe:

Peclet number

\(N\) :

Radiation variable

\(B_{{\text{e}}}\) :

Bejan number

\(\mu\) :

Dynamic viscosity

\(\alpha_{0}\) :

Mean radiation absorption coefficient

Ns:

Entropy generation

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Acknowledgements

The authors acknowledge the financial support provided by the Center of Excellence in Theoretical and Computational Science (TaCS-CoE), KMUTT. The first author appreciates the support provided by Petchra Pra Jom Klao Ph.D. Research Scholarship through grant no (95/2563), by King Mongkut’s University of Technology Thonburi, Thailand.

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Authors and Affiliations

  1. Fixed Point Research Laboratory, Fixed Point Theory and Applications Research Group, Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Dolat Khan, Poom Kumam, Wiboonsak Watthayu & Amir Khan

  2. Center of Excellence in Theoretical and Computational Science (TaCS-CoE), Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), 126 Pracha Uthit Rd., Bang Mod, Thung Khru, Bangkok, 10140, Thailand

    Dolat Khan & Poom Kumam

  3. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan

    Poom Kumam

  4. Department of Mathematics, City University of Science and Information Technology, Peshawar, KPK, Pakistan

    Ata ur Rahman

  5. Mechanical Engineering Department, College of Engineering, Prince Sattam Bin Abdulaziz University, 11991, Wadi Addawaser, Saudi Arabia

    Ahmed M. Galal

  6. Production Engineering and Mechanical Design Department, Faculty of Engineering, Mansoura University, P.O 35516, Mansoura, Egypt

    Ahmed M. Galal

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  1. Dolat Khan
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Contributions

DK models the problem. DK solved the modeled problem analytically. DK and AR draw the graphs. Results and discussions have reviewed by AR, AMG, and WW reviewed the whole manuscript. Proof reading has performed by PK and AK.

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Correspondence to Poom Kumam.

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Khan, D., ur Rahman, A., Kumam, P. et al. Relative magnetic field analysis on Casson dusty fluid of two-phase fluctuating flow over a parallel plate: second law analysis. J Therm Anal Calorim 148, 3659–3670 (2023). https://doi.org/10.1007/s10973-023-11953-4

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  • DOI: https://doi.org/10.1007/s10973-023-11953-4

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